Critical population and error threshold on the sharp peak landscape for a Moran model / Raphaël Cerf.

Format:

Book

Author/Creator:

Cerf, Raphaël, author.

Series:

Memoirs of the American Mathematical Society ; Volume 233, Number 1096 (second of 6 numbers)

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 233, Number 1096 (second of 6 numbers)

Language:

English

Subjects (All):

Molecular dynamics--Mathematical models.

Molecular dynamics.

Macromolecules--Mathematical models.

Macromolecules.

Chromosome replication--Mathematical models.

Chromosome replication.

Physical Description:

1 online resource (87 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size m of chromosomes of length \ell over an alphabet of cardinality \kappa. The mutation probability per locus is q. He deals only with the sharp peak landscape: the replication rate is \sigma>1 for the master sequence and 1 for the other sequences. He studies the equilibrium distribution of the process in the regime where \ell\to +\infty,\qquad m\to +\infty,\qquad q\to 0, {\ell q} \to a\in ]0,+\infty[, \qquad\frac{m}{\ell}\to\alpha\in [0,+\infty].

Contents:

""Cover""; ""Title page""; ""Chapter 1. Introduction""; ""Chapter 2. The Model""; ""Chapter 3. Main Results""; ""Chapter 4. Coupling""; ""Chapter 5. Normalized Model""; ""Chapter 6. Lumping""; ""6.1. Distance process""; ""6.2. Occupancy process""; ""6.3. Invariant probability measures""; ""Chapter 7. Monotonicity""; ""7.1. Coupling of the lumped processes""; ""7.2. Monotonicity of the model""; ""Chapter 8. Stochastic Bounds""; ""8.1. Lower and upper processes""; ""8.2. Dynamics of the bounding processes""; ""8.3. A renewal argument""; ""8.4. Bounds on ""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1964-5